1. Atomic Structure and Atomic Spectra
Chapter 13

2. Table 10.1 Hydrogenic radial wavefunctions
R = (Nn,l) (polynomial in r) (decaying exponential in r)
Ln,l(p) is an associated
Laguerre polynomial

3. Fig 10.4

4. Potential energy between an electron and proton
in a hydrogen atom + - + - + - ao
One-electron wavefunction = an atomic orbital

5. Fig 10.5 Energy levels of a hydrogen atom
Unbound
states
in cm-1
Principle quantum number
n = 1, 2, 3,...,∞
Angular momentum QN
l = 0, 1, 2,..., (n-1)
Magnetic QN
ml = -l, ..., +l
Spin QN
ms = ±1/2
Bound
states

6. Fig 10.7 Energy of orbitals in a hydrogenic atom
Energy only depends on principal quantum number n
n=3
n=2
En = -RH
( ) 1 n2
Why the degeneracy?!
n=1

7. Fig 10.9 Balance of kinetic and potential energies that
accounts for the ground state of hydrogenic atoms

8. Fig 10.10 Electron densities of 1s and 2s orbitals
in a hydrogen atom

9. Fig 10.11 Boundary surface of an s-orbital within which
there is a 90% probability of finding Mz. Electron
r90
Orbitals don’t have edges!

10. spherically symmetrical
Fig Probability density for an s-orbital
s-orbital is
spherically symmetrical

11. Fig 10.14 Radial distribution function for an s-orbital

12. Fig 10.15 Boundary surfaces for p-orbitals
ml = -1
ml = 0
ml = 1

13. Fig 10.16 Boundary surfaces for d-orbitals
ml = -2
ml = -1
ml = 0
ml = 1
ml = 2

14. Fig 10.17 Grotrian diagram for the spectrum of H
A photon can carry only one unit
of angular momentum
Some transitions are allowed,
other are forbidden
Selection rules for allowed
transitions:
Δl = ±1 and Δml = 0, ±1